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Why does a call option move only about 40 cents when the stock moves $1?
Delta: a call with a delta of 0.40 gains about 40 cents per share when the stock rises $1, because its strike sits above the stock price.
Why does an option lose value when the stock doesn't move?
Theta: an option's time value shrinks a little every day, so with the stock flat its price drifts lower, and the drain speeds up near expiry.
Why does an option worth $0, if exercised today, still cost $3.80?
An out-of-the-money option has no intrinsic value, so its whole price is time value: what the market pays for the chance of a move before expiry.
Why can a call option expire worthless even if the stock goes up 7%?
A call has value at expiry only above its strike and covers its cost only above break-even, so a 7% rise can still leave it at zero.
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